The man who drove a van into a crowd in the German city of Munster was well-known to police and had a history of run-ins with the law, German prosecutors said, adding that they believe he acted alone.
The 48-year-old, whose name was not released, killed two people and injured 20 others on Saturday afternoon outside a bar in the city's old town before shooting himself dead inside the van.
He was a Munster resident and apparently well off.
The city's police president, Hajo Kuhlisch, said the man's four apartments - two in Munster and two in Saxony - and several cars had been searched thoroughly, but officers were still investigating the evidence and it was too early to speculate about a motive.
"We have no indications that there is a political background or that others were involved," prosecutor Elke Adomeit told reporters. "But he was well known to the police."
She said the man had three previous court procedures in Munster and one in nearby Arnsberg in 2015 and 2016.
His run-ins with the law regarded threats, property damage, fraud and a hit-and-run, but Ms Adomeit said all charges were dismissed.
Local media have identified the man as an industrial designer who had been suffering psychological problems, but police would not confirm the details.
Authorities have identified the two victims killed by the van as a 51-year-old woman from Luneburg county, 180 miles to the north east, and a 65-year-old man from nearby Borken county.
Early on Sunday, all three bodies were taken from the crash scene in front of the well-known Kiepenkerl pub.
The silver-grey van was hauled away hours later after explosives experts had thoroughly checked it.
Inside the van, police found illegal firecrackers that were disguised as a fake bomb, a fake pistol and the real gun the driver used to kill himself with.
Inside the apartment where the man was living, which was near the crash scene, police found more firecrackers and a "no-longer usable AK-47 machine gun".
Officials said some of the 20 people injured were still in a life-threatening condition. They have not identified them, but said that people from the Netherlands are among them.
Armin Laschet, the governor of North Rhine-Westphalia state where Munster is located, toured the city on Sunday.
"This was a horrible and sad day for the people of Munster, all of Germany ... and also the people of the Netherlands, who were sitting here and became victims," he said.
He did not elaborate on how many Dutch were injured or how serious the injuries were.
The local daily Muenstersche Zeitung reported that the perpetrator had vaguely announced his suicide plans a week ago in an email to friends, but police would not confirm the details.
Munster is a popular tourist destination with 300,000 inhabitants, known for its medieval old town, which was rebuilt after massive destruction during the Second World War.
The city was buzzing on Saturday - one of the first warm spring days of the year - and people were sitting outside the famous Kiepenkerl pub when the van was driven into the bar's tables with such force that the vehicle only stopped when it hit the pub's wall.
Police quickly evacuated the area and ambulances, firefighters and helicopters rushed to the scene to aid the injured.
Interior minister Horst Seehofer, who visited the crash scene with Mr Laschet on Sunday and placed flowers there, said "this cowardly and brutal crime has shocked all of us".
The city's Roman Catholic bishop, Felix Glenn, invited all of Munster's citizens to a joint Catholic-Lutheran memorial service at the famous Paulus Cathedral on Sunday night.